Question

Rút gọn biểu thức \(\dfrac{x+\sqrt{x}-2}{\sqrt{x}+2}\) với \(x\ge0\) 

Answer 1

\(\Leftrightarrow\dfrac{x+\sqrt{x}+2-4}{\sqrt{x}+2}\)

\(\Leftrightarrow\dfrac{\left(x-4\right)+\left(\sqrt{x}+2\right)}{\sqrt{x}+2}\)

\(\Leftrightarrow\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)+\left(\sqrt{x}+2\right)}{\sqrt{x}+2}\)

\(\Leftrightarrow\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2+1\right)}{\sqrt{x}+2}\)

\(\Leftrightarrow\sqrt{x}-2+1\)

\(\Leftrightarrow\sqrt{x}-1\)